Changing Math Classes Through Curriculum

Why does curriculum in early-grades math matter? And when a federally sponsored study comes out that appears to favor two types of curricula in particular, how should we interpret it?

A researcher, a college professor, and the head of prominent education advocacy group came together at a forum in Washington yesterday to hash it out.

The starting point for their discussion was a study conducted by Mathematica Policy Research, which found that a pair of elementary math programs, Saxon Math and Math Expressions, had an edge over two others in producing gains in boosting student achievement. (See my colleague Debbie Viadero's story on the report, from earlier this year.) Among the legions of parents, teachers, mathematicians, and policy experts who love to debate the quality of various math curricula, those results produced plenty of chatter.

On Tuesday, the author of that study, Robert Agodini of Mathematica, as well as two others taking part in a panel discussion, cautioned against drawing overly broad conclusions from the document, noting that it's only the first step in an extended research project. The two panelists, Mary Lindquist and Kati Haycock, were similarly circumspect, though all of them seemed to agree that it was just the sort of study that is desperately needed, as teachers and school officials search for answers on how to improve the quality of teaching and learning in math in this country. Curriculum, undeniably, is a big part of that, they said.

In general, the study found that, within a cohort of 1,300 1st graders from 39 schools, students who used Saxon Math and Math Expressions significantly outperformed those using Investigations in Number, Data, and Space, as well as Scott Foresman-Addison Wesley Mathematics. A description handed out at the event offered this general description of the programs: Saxon is a more scripted curriculum with more teacher-directed lessons; Investigations tends to be more student-centered; Math Expressions is sort of a hybrid approach;and the Scott-Foresman model combines a focus on math fundamentals, teacher-directed instruction, and “differentiated” materials for different students. Seven math curriculum programs, including the four he studied, represent 91 percent of the market for grades K-2, Agodini said at the forum.

Lindquist, a professor emeritus at Columbus College in Georgia, is the former president of the National Council of Teachers of Mathematics. She noted the study's limitationsit only evaluated students on one test, for one year, in one grade. Those caveats tend to get lost in the public sphere, though. “I get on the Web and see ‘Two Winners,’ ” Lindquist said. “I’m anxious to see what happens [in the study] after five years.”

Haycock, as many Ed Week readers know, is the president of the Education Trust, which seeks to close the gap between low- and high-achieving students. She was similarly circumspect about the direct implications of the study, though she hoped it would prompt a broader discussion about improving teaching and learning in early-grades math. State math standards are too vague, she said. A big complaint among educators in the No Child Left Behind era is that schools promote teaching to the test. But if teachers aren't given good direction on what to teach through good curriculum, "frankly, it's no wonder" tests drive instruction, Haycock said.

"There is a sense of desperation among teachers for quality curriculum," Haycock said. "Teachers feel like, essentially, they are teaching in the dark."

Lindquist agreed. "Teachers are busy," she said, and at the elementary level, "they aren't experts in every subject." Without guidance through a good curriculum, teachers become reliant on bulky textbooks, said Lindquist, who cited a personal example.

"I know when I started teaching, I moved through the book," she said. "I don't know where my students were, but I was moving through the book."

In recent years, there have been a number of efforts to clarify, and simplify, the work of elementary teachers. The NCTM in 2006 released "Curriculum Focal Points," a document that seeks to guide teachers in elementary and middle-grades math. The National Mathematics Advisory Panel, commissioned by the White House, called for educators to focus on major topics, like fractions and whole numbers, to prepare students for algebra.

What is the value of good math curriculum, for teachers, for schools? And what sorts of questions about early-grades math curriculum should the federal government be attempting to answer, through studies like the one by Mathematica?

I am a teacher with over 30 years of experience in the class room. Many of those years were spent teaching all levels of math from 7th grade through geometry.

I currently work at an elementary school that uses Saxon Math and I have problems with that curriculum. In grades 4-6, the text will introduce a new concept and then the problems that follow have nothing to do with that concept. I understand the need for constant review, but believe that assignments should concentrate on the new material and incorporate the old.

In grades k-3, there is too much emphasis on being fast. Students are required to complete 100 facts in less than 5 minutes. This is too much for the younger students who are still struggling to write (draw?) their numbers correctly. This leads to frustration and "shutting down;" especially when the teachers count the grades on these "timed" tests as 50% of a student's grade.

Singapore Math doesn't use flash cards. Students learn 9+6 = 10+5 = 15. Students actually go slower with this approach, but they learn the role of tens far better. In short, number sense is improved. How does one say this politely: The focus on speed in addition and multiplication tables is just plain stupid.

I used to believe that timed tests caused too much pressure on small children in math. I have since changed my mind. My daughters used to have a lot of stress over timed tests, but their teachers placed too much emphasis on their results. My son, on the other hand, was in a school that just used them as a goal. Every class in the school did a timed test on Thursday mornings and each time a student completed a level, he or she got to color one element of a banana split picture. At the end of the year, the students who had completed their picture got to attend an ice cream social. There was no pressure as far as grades, just an intrinsic reqard. My son learned his math facts inside and out and is much better than I am at his times tables. I am now a firm believer!

The focus on speed is not at all stupid. The student who is fluent in computation has a huge advantage in math later on. We used to do 100 multiplication problems in two minutes at the start of every day in fifth grade; it was no big deal.